Acombination lock uses three numbers between 1 and 78 with repetition, and they must be selected in the correct sequence. which of the five counting rules is used to find that number? how many different "combinations" are possible? is the name of "combination lock" appropriate? if not, what other name would be better?

  first number      and       second number       and     third number   =     Total

78 possibilities      x         78 possibilities           x     78 possibilities   =     234

Since "order" matters, this is a permutation.

So, this can be calculated using: ₇₈P₃

"Permutation lock" would be a more appropriate name.

Step-by-step explanation:

According to the problem, the lock uses three numbers between 1 and 78, that is, 77 elements in total, with repetition. To find the answer we have to use the definition that allow elements to repeat, which is:

; where is the total number of elements, and is the subgroup.

Replacing values, we have:

Therefore, there are 456,533 ways to use the lock.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.